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Special Right Triangles

Explore the properties of special right triangles and learn ratios of sides. Wallpaper tiling, missing side calculations. Perfect for studying 45-45-90 and 30-60-90 triangles. Enhance your geometry skills with comprehensive examples and exercises.

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Special Right Triangles

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  1. We make a living by what we get, but we make a life by what we give. -- Winston Churchill Special Right Triangles Chapter 8 Section 3 Learning Goal: Use properties of 45°-45 °-90 °, and 30 °-60 °-90 ° Triangles

  2. 45°-45°-90° Triangles x • Special Right Triangle 45° d2 =x2 + x2 d Simplify: d2 =2x2 x √d2 =√ 2x2 d=x√ 2 Three sides of lengths x, x, x√2 What did we learn about ratios of sides? Ratio of a 45°-45°-90° triangle is: 1 : 1 : √2

  3. 45°-45°-90° Triangles 45° 6√2 • Find the missing side 6 a = 4√2 cm

  4. 45°-45°-90° Triangles 3 8 45° 21 14

  5. Special Right Triangles WALLPAPER TILING The wallpaper in the figure can be divided into four equal square quadrants so that each square contains 8 triangles. What is the area of one of the squares if the hypotenuse of each 45°–45°–90° triangle measures millimeters? A = 24.5 mm

  6. 30°-60°-90° Triangles Consider an equilateral ∆ 30° a2 =(2x)2 – x2 2x 2x Simplify: a2 =4x2 – x2 a a2 =3x2 √a2 =√3x2 60° 60° x x a=x√3 Three sides of lengths x, 2x, x√3 Ratio of a 30°-60°-90° triangle is: Ratios of sides? 1 : √3 : 2

  7. 30°-60°-90° Triangles • Find the missing sides 4 60° 10 5 8√3 3 30° 5√3

  8. 30°-60°-90° Triangles 60° 30° 8 6 60° 4√2 Find the Altitude of the Δ

  9. Special Right Triangles Refer to the figure. Find x and y.

  10. Special Right Triangles The length of the diagonal of a square is cm. Find the perimeter of the square. 60 cm

  11. Special Right Triangles The side of an equilateral triangle measures 21 inches. Find the length of an altitude of the triangle.

  12. Homework Special Right Triangles 45-45-90, 30-60-90

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